Term Independent of x

Q.

Prove the there is no term containing $x^{10}$ in the expansion of ${(x^2-\frac{2}{x})}^{18}$

Q. If $(1+2x+3x^2{)}^{10}=a_0+a_{1}x+a_2{x}^2+...+a_{20}{x}^{20},$ then $a_1$ equals

1. $10$
2. $20$
3. $210$
4. $110$

Q. The term independent of $x$ in the expansion ${(\frac{\sqrt{x}}{\sqrt{3}}+\frac{\sqrt{3}}{2x^2})}^{10}$ is equal to:

1. $\frac{7}{12}$
2. $\frac{1}{3}$
3. $\frac{4}{7}$
4. $\frac{5}{12}$

Q. If sum of the coefficients of first, second and third terms in the expansion of ${(x^2+\frac{1}{x})}^m$ is $46,$ then the coefficient of the term that is independent of $x,$ is

1. $96$
2. $84$
3. $78$
4. $88$

Q. The term independent of $x$ in the expansion of $(1+x+2x^3){(\frac{3x^2}{2}-\frac{1}{3x})}^9$ is

1. $\frac{17}{54}$
2. $\frac{17}{52}$
3. $\frac{19}{54}$
4. $\frac{19}{52}$

Q. The ratio of coefficient of $x^{15}$ to the term independent of $x$ in the expansion of ${(x^2+\frac{1}{2x})}^{15}$ is

1. $16:1$
2. $1:32$
3. $1:16$
4. $32:1$

Q.

$3^{2\times 100+1}+2^{100+2}$ is divisible by________.

1. 5

2. 6

3. 7

4. 8

Q. The term independent of $x$ in expansion of
${(\frac{x+1}{x^{2/3}-x^{1/3}+1}-\frac{x-1}{x-x^{1/2}})}^{10}$is

1. 4
2. 120
3. 210
4. 310

Q. The term independent of $x$ in the expansion of
${(\sqrt{\frac{x}{3}}+\sqrt{\frac{\sqrt{3}}{x^2}})}^{10}$ is

1. $5/9$
2. $5/3$
3. $1/3$
4. $4/3$

Q. Find the coefficient of $x^2{y}^5$ in the expansion of $(3+2x-y{)}^{10}$.

Q. The term independent of x in the expansion of $(1+x{)}^n{(1+\frac{1}{x})}^n$ is

1. $C_0^2+2C_1^2+3C_2^2+....+(n+1)C_n^2$
2. $(C_0+c_1+....+c_n{)}^2$
3. $c_0^2+C_1^2+.....+c_n^2$
4. $Noneoftheabove$

Q. If sum of the coefficients of first, second and third terms in the expansion of ${(x^2+\frac{1}{x})}^m$ is $46,$ then coefficient of the term that is independent of $x$ is

1. $96$
2. $84$
3. $78$
4. $88$

Q. The maximum value of the term independent of $t$ in the expansion of ${(t{x}^{1/5}+\frac{(1-x{)}^{1/10}}{t})}^{10}$ where $x\in (0,1)$ is :

1. $\frac{10!}{\sqrt{3}(5!{)}^2}$
2. $\frac{2\times 10!}{3(5!{)}^2}$
3. $\frac{10!}{3(5!{)}^2}$
4. $\frac{2\times 10!}{3\sqrt{3}(5!{)}^2}$

Q. The coefficient of the term independent of $x$ in the expansion of ${(\frac{x+1}{x^{2/3}-x^{1/3}+1}-\frac{x-1}{x-x^{1/2}})}^{10}$

1. $210$
2. $105$
3. $70$
4. $110$